Question

If $19$th term of a non-zero A.P. is zero, then its ($49$th term) : ($29$th term) is :

• A. $4:1$
• B. $1:3$
• C. $2:1$
• D. $3:1$

Answer 1

The correct option is D $3:1$

$T_{19}=0$
$\Rightarrow a+18d=0$
$\Rightarrow a=-18d$
$\Rightarrow \frac{T_{49}}{T_{29}}=\frac{a+48d}{a+28d}=\frac{-18d+48d}{-18d+28d}\therefore \frac{T_{49}}{T_{29}}=\frac{3}{1}$